Question

What is the length of a diagonal of a square with a side length of 8? A.4 B.4√2 C.4√3 D.8√2

Answer 1

Explanation:

A square by definition has sides all the same length. I know you know this. The diagonal of a square forms the hypotenuse of a right triangle that is, to be specific, a 45-45-90 right triangle. The height of the right triangle is 8 (one of the side lengths of the square), and the base of the right triangle is 8 (another of the side lengths of the square), and the diagonal, as already stated, is the hypotenuse. We can use Pythagorean's Theorem to solve for the length of the hypotenuse:

and

and

so

Now we just need to find the largest perfect square that multiplied by another number (preferably a prime number) that gives us 128. I do believe that 64 * 2 = 128, and 64 is the largest perfect square that goes into 128 evenly. 2 is prime. Simplifying our value for c:

which simplifies finally to

That is the length of the diagonal of that square.

Answer 2

Explanation:

A square by definition has sides all the same length. I know you know this. The diagonal of a square forms the hypotenuse of a right triangle that is, to be specific, a 45-45-90 right triangle. The height of the right triangle is 8 (one of the side lengths of the square), and the base of the right triangle is 8 (another of the side lengths of the square), and the diagonal, as already stated, is the hypotenuse. We can use Pythagorean's Theorem to solve for the length of the hypotenuse:

`8^2+8^2=c^2` and

`64+64=c^2` and

`c^2=128` so

`c=√(128)`

Now we just need to find the largest perfect square that multiplied by another number (preferably a prime number) that gives us 128. I do believe that 64 * 2 = 128, and 64 is the largest perfect square that goes into 128 evenly. 2 is prime. Simplifying our value for c:

`c=√(64*2)` which simplifies finally to

`c=8√(2)`

That is the length of the diagonal of that square.